1. 3/5/2016Agenda Textbook / Web Based ResourceTextbook / Web Based Resource –Arithmetic Sequences –Formula of Arithmetic Sequence –Partial Sums of Arithmetic Sequence ClassworkClasswork INSERT HERE HomeworkHomework INSERT HERE

2. 3/5/2016 Arithmetic Sequences and Partial Sums

3. 3/5/2016 By the end of the day You should know how to: Determine if a sequence is arithmeticDetermine if a sequence is arithmetic Find the common difference of an arithmetic sequence.Find the common difference of an arithmetic sequence. Write the first 5 terms of an arithmetic sequence from an explicit or recursive formulaWrite the first 5 terms of an arithmetic sequence from an explicit or recursive formula Find an nth partial sum given a sequence or summation notation.Find an nth partial sum given a sequence or summation notation.

4. 3/5/2016 Arithmetic Sequences A sequence is arithmetic if the difference between consecutive terms is always the same.A sequence is arithmetic if the difference between consecutive terms is always the same. The difference between the terms is called the common difference.The difference between the terms is called the common difference.

5. 3/5/2016 Arithmetic Sequences The nth term is of an arithmetic sequence can be found by: Explicit Formula: a n = dn + c d = common difference n = # of the term c = a 1 – d Recursive Formula: a n+1 = a n + d a n+1 = next term a n = current term d = common difference

6. 3/5/2016 Arithmetic Sequences Explicit Formula: a n = 3n – 2 a n = 3(1) – 2, 3(2) – 2, 3(3) – 2, 3(4) – 2,… a n = 1, 4, 7, 10, … Recursive Formula: a 1 = 1, a n+1 = a n + 3 a n = 1, 1+3, (1+3)+3, [(1+3)+3]+3… a n = 1, 4, 7, 10, …

7. 3/5/2016 Arithmetic Sequences You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

8. 3/5/2016 Partial Sum The sum of the first n terms of a finite arithmetic sequence can be found by: If a n = 3n – 2, find S 4 : n = 4 a 1 = 1 a n = a 4 = 10

9. 3/5/2016 Partial Sum Why does this work? S 4 = 1 + 4 + 7 + 10 1111 What if there’s an odd number of terms? S 5 = 1 + 4 + 7 + 10 + 13 1414

10. 3/5/2016 Partial Sum Find: Arithmetic Sequence

11. 3/5/2016 Partial Sum You Try These on Your Own: 1.INSERT YOUR PROBLEMS HERE

12. 3/5/2016 It’s the end of the day Do you know how to: Determine if a sequence is arithmetic?Determine if a sequence is arithmetic? Find the common difference of an arithmetic sequence?Find the common difference of an arithmetic sequence? Write the first 5 terms of an arithmetic sequence from an explicit or recursive formula?Write the first 5 terms of an arithmetic sequence from an explicit or recursive formula? Find an nth partial sum given a sequence or summation notation?Find an nth partial sum given a sequence or summation notation?

13. 3/5/2016Homework Study: INSERT HERE Do: Read & Take Notes: INSERT HERE

14. 3/5/2016 Resource Credits Justin Bohannon Justin Bohannon Justin Bohannon